Solve by Substitution 3x-7y=1 , -6x+14y=-2

Problem

{[3*x−7*y=1],[−6*x+14*y=−2])

Solution

1. Solve the first equation for x by adding 7*y to both sides and dividing by 3

3*x=1+7*y

x=(1+7*y)/3

2. Substitute the expression for x into the second equation.

−6*((1+7*y)/3)+14*y=−2

3. Simplify the equation by distributing the −6 and dividing by 3

−2*(1+7*y)+14*y=−2

−2−14*y+14*y=−2

4. Combine like terms to observe the resulting identity.

−2=−2

5. Interpret the result, noting that since the statement is always true, the two equations represent the same line.

Final Answer

Infinite solutions of the form *(x,(3*x−1)/7)

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